DLMF:15.5.E19 (Q5036)

From DRMF
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:15.5.E19
No description defined

    Statements

    Defining formula
    z ⁢ ( 1 - z ) ⁢ ( a + 1 ) ⁢ ( b + 1 ) ⁢ F ⁡ ( a + 2 , b + 2 ; c + 2 ; z ) + ( c - ( a + b + 1 ) ⁢ z ) ⁢ ( c + 1 ) ⁢ F ⁡ ( a + 1 , b + 1 ; c + 1 ; z ) - c ⁢ ( c + 1 ) ⁢ F ⁡ ( a , b ; c ; z ) = 0 . 𝑧 1 𝑧 𝑎 1 𝑏 1 Gauss-hypergeometric-F 𝑎 2 𝑏 2 𝑐 2 𝑧 𝑐 𝑎 𝑏 1 𝑧 𝑐 1 Gauss-hypergeometric-F 𝑎 1 𝑏 1 𝑐 1 𝑧 𝑐 𝑐 1 Gauss-hypergeometric-F 𝑎 𝑏 𝑐 𝑧 0 {\displaystyle{\displaystyle{z(1-z)(a+1)(b+1)}F\left(a+2,b+2;c+2;z\right)+{(c-% (a+b+1)z)(c+1)}F\left(a+1,b+1;c+1;z\right)-{c(c+1)}F\left(a,b;c;z\right)=0.}}
    0 references
    DLMF id
    DLMF:15.5.E19
    0 references
    Symbols used
    $$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function
    Defining formula
    F ⁡ ( a , b ; c ; z ) Gauss-hypergeometric-F 𝑎 𝑏 𝑐 𝑧 {\displaystyle{\displaystyle F\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)}}
    xml-id
    C15.S2.E1.m2aqdec
    0 references
    Q11644
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C15.S1.XMD3.m1rdec
    0 references
    Q11645
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C15.S1.XMD4.m1qdec
    0 references
    Q11646
    Defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C15.S1.XMD5.m1qdec
    0 references
    Q11647
    Defining formula
    c 𝑐 {\displaystyle{\displaystyle c}}
    xml-id
    C15.S1.XMD6.m1qdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q5036&oldid=41575"